Origen

Early 17th century: from cock1 + tail1. The original use was as an adjective describing a creature with a tail like that of a cock, specifically a horse with a docked tail; hence (because hunters and coach-horses were generally docked) a racehorse which was not a thoroughbred, having a cock-tailed horse in its pedigree (early 19th century). sense 1 (originally US, also early 19th century) is perhaps analogous, from the idea of an adulterated spirit.

The original use of cocktail was as a term to describe a creature with a tail like that of a cock, in particular a horse with a docked tail. Hunting horses and stagecoach horses generally had their tails shortened in this way, which led to the term being applied to a racehorse which was not a thoroughbred but ‘of mixed blood’, with a cock-tailed horse somewhere in its pedigree. It may be that the current sense of an alcoholic drink with a mixture of ingredients, which dates from the early 19th century, comes from this use, though the exact origin of the term is much debated.